{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3dff3e79-12b9-4b56-b5a7-6603fb99afd8",
   "metadata": {},
   "source": [
    "Chapter 8\n",
    "# 具有相关性的随机行走\n",
    "Book_6《数据有道》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c867fbf3-9f97-44ff-942d-59c1cd227896",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "976a125a-0e50-4604-8fcc-8fcf8ca1c769",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_steps = 200; \n",
    "# number of steps\n",
    "\n",
    "mu_1 = 0.2\n",
    "mu_2 = 0.3\n",
    "\n",
    "mu = np.matrix([mu_1, mu_2])\n",
    "\n",
    "sigma_1 = 1\n",
    "sigma_2 = 2\n",
    "rho_1_2 = 0.8\n",
    "delta_t = 1\n",
    "\n",
    "SIGMA = np.matrix([[sigma_1**2, sigma_1*sigma_2*rho_1_2],\n",
    "                   [sigma_1*sigma_2*rho_1_2, sigma_2**2]])\n",
    "\n",
    "L = np.linalg.cholesky(SIGMA)\n",
    "R = L.T\n",
    "\n",
    "Z = np.random.normal(size = (N_steps,2))\n",
    "\n",
    "delta_X = mu*delta_t + Z@R*np.sqrt(delta_t)\n",
    "\n",
    "X = np.cumsum(delta_X, axis = 0); \n",
    "\n",
    "X_0 = np.zeros((1,2))\n",
    "X = np.vstack((X_0,X))\n",
    "\n",
    "t_n = np.linspace(0,N_steps,N_steps+1,endpoint = True)*delta_t\n",
    "\n",
    "rows = 1\n",
    "cols = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "00b843a2-a059-4ba6-acfa-3f9b827bb6b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 't')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax= plt.subplots()\n",
    "\n",
    "ax.plot(t_n, X, lw=1)\n",
    "ax.plot(t_n, mu_1*t_n,color = 'r', lw=0.25)\n",
    "ax.plot(t_n, mu_2*t_n,color = 'r', lw=0.25)\n",
    "\n",
    "ax.set_xlim([0,N_steps])\n",
    "# ax.set_ylim([-20,100])\n",
    "# ax.set_yticks([-20, 0, 20, 40, 60, 80])\n",
    "ax.set_xlabel('t')\n",
    "#%% scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "94c1b18e-935c-413c-b209-43b09f74f32d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "delta_X_df = pd.DataFrame(data=delta_X, columns=[\"Delta x1\", \"Delta x2\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "637232df-dc0f-4f3b-a525-e06e7ae4c8d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x1e0ada25ab0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax= plt.subplots()\n",
    "\n",
    "# ax.scatter([delta_X[:,0]],[delta_X[:,1]])\n",
    "sns.jointplot(data = delta_X_df, x = \"Delta x1\", y = \"Delta x2\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
